How do you evaluate 4log_4 6 - log_4 5?

1 Answer
May 29, 2015

Use the following properties of logs:
1] alogx=logx^a
2] logx-logy=log(x/y)
So in your case:
log_4(6^4)-log_4(5)=log_4(6^4/5)=log_4(259.2)=x
so:
4^x=259.2
if x=4
4^4=256
if x=4.002
4^(4.002)=259.2

Another thing that you can do is to change base (using, for example, natural logs) as:
log_4(259.2)=ln(259.2)/(ln(4))=4.0089